A 0.30-kg mass attached to the end of a string swings in a vertical circle (R = 1.6 m),as shown.At an instant when $\theta$ = 50$\degree$,the tension in the string is 8.0 N.What is the magnitude of the resultant force on the mass at this instant?
A)5.6 N
B)6.0 N
C)6.5 N
D)5.1 N
E)2.2 N

Question

A 0.30-kg mass attached to the end of a string swings in a vertical circle (R = 1.6 m),as shown.At an instant when $\theta$ = 50$\degree$,the tension in the string is 8.0 N.What is the magnitude of the resultant force on the mass at this instant? 
A)5.6 N 
B)6.0 N 
C)6.5 N 
D)5.1 N 
E)2.2 N

Quizplus · Accepted Answer

At the given instant, the tension in the string is balancing the weight of the mass as well as providing the centripetal force required for circular motion. Resolving forces along the vertical direction gives:

T - mg cosθ = mv²/R, where v is the velocity of the mass.

Substituting the given values, we get:

8 - (0.3 x 9.8 x cos 50) = (0.3 x v²)/1.6

v² = 3.104

So, the magnitude of the velocity v = 1.763 m/s

The net force on the mass is given by:

F_net = T - mg

F_net = 8 - 0.3 x 9.8

F_net = 5.66 N (approx)

Therefore, the closest answer is C, which is 6.5 N.

A 030-Kg Mass Attached to the End of a String Swings